Maximum Likelihood Estimate

I need help with this question :

Suppose a town has bicycles with license numbers 1, . . . , N . You observe
5 bicycles and the highest number you observe is 60. What is the MAximum Likelihood Estimate(MLE) for the number of bicycles in the town? Does the MLE provide a reasonable estimate?

Suppose a town has bicycles with license numbers 1, . . . , N . You observe
5 bicycles and the highest number you observe is 60. What is the MAximum Likelihood Estimate(MLE) for the number of bicycles in the town? Does the MLE provide a reasonable estimate?

Let be a random sample of five observations from a discrete uniform distribution with pdf . The largest observation is 60 (that is, ).

Then .

Note that L is a monotonically decreasing function of N and so nowhere in the interval is equal to zero. However, note that: